# Combined Gas Law Formula: Concept, Derivation, Explanation

The three gas laws are integrated into a single one known as the combined gas law. These three laws are Charles', Gay-Lussac, and Boyle's Law. Combined Gas Law Formula expresses the relationship between a set amount of gas's pressure, volume, and absolute temperature. The Combined Gas Law Formula expresses the relationship between a set amount of gas’s pressure, volume, and absolute temperature. The quantity of gas is the single constant in a combined gas law problem.

The present-day refrigerator utilizes gas laws to remove heat from a system. The coils’ compressed gas is given room to expand. As a result of this expansion, the gas’s temperature decreases, and the gas receives heat energy from the materials inside the refrigerator. The pressure on the gas compresses it and boosts its temperature as it is fed through the coils. The heat is subsequently released into the atmosphere through the coils. The procedure is repeated as new compressed gas is pushed through the system.

## Introduction to Combined Gas Law Formula

The three gas laws are integrated into a single one known as the combined gas law. These three laws are Charles’, Gay-Lussac, and Boyle’s Law.

According to this rule, the ratio of the gas’s absolute temperature to the product of its volume and pressure is a constant. The ideal gas law is produced when Avogadro’s law is added to the combined gas law, which is particularly notable. The combined gas law has no recognized discoverer.

## Combined Gas Law Formula

The combined gas law investigates the behavior of a fixed volume, constant pressure, and/or constant gas temperature.

The combined gas law may be expressed mathematically in the following manner:

k = PV/T

In other words, a constant results from multiplying pressure by volume and dividing it by temperature.

The law is typically utilized to contrast the before-and-after situations, nevertheless. This is how the combined gas law is written:

PiVi/Ti =PfVf/Tf where

The initial Pressure is Pi.

The initial volume is Vi.

The initial absolute temperature is Ti.

The final pressure is Pf.

The final volume is Vf.

The final absolute temperature is Tf.

It is crucial to remember that the temperatures are absolute temperatures measured in Kelvin, NOT degrees Celsius or degrees Fahrenheit. It’s crucial to maintain consistency with the units as well.

## Uses Of Combined Gas Law Formula

The combined gas law has useful applications when working with gases at typical temperatures and pressures. The accuracy of this gas law decreases with increasing temperature and pressure, much as other gas laws based on ideal behavior. The law is applied in fluid mechanics and thermodynamics. For instance, it may be used to determine the volume, temperature, or pressure of the gas in clouds to forecast the weather.

Practical uses of the combined gas law may be found in daily life. It is applicable anytime pressure, volume, and temperature vary while the amount of gas is constant. For instance, the rule may anticipate how air conditioners, refrigerators, and clouds behave. It is also used in other computations involving fluid mechanics and thermodynamics.

The combined gas law barely approximates the behavior of real gases since it is an ideal gas law. At high temperatures and pressures, the law loses accuracy.

## Derivation Of The Combined Gas Law Formula

The three previously established laws, Boyle’s law PV=K, Charles’s law V/T=K, and Gay-Lussac’s law P/T=K, are combined to form the combined gas law. Consequently, PV/T=K is the combined gas law’s formula.

P is for pressure, T is for temperature, V is for volume, and K is constant.

The combined gas law’s formula can be changed to compare two sets of circumstances in a single material. The values for temperature (T), pressure (P), and volume (V) in the equation with subscripts of one are representative of the beginning state. Additionally, those with a subscript of two accurately represent the final state.

P1V1/T1 =P2V2/T2

## Problem Based On Combined Gas Law Formula

Find the volume of the gas at 760.0 mm Hg pressure and 273 K when 2.00 liters are collected at 745.0 mm Hg and 25.0 °C.

To begin, change 25.0 °C to Kelvin. You get 298 Kelvin as a result.

The combined gas law formula should then be updated with the values. Mixing up which numbers go together is the most frequent error learners make. It helps to prevent this mistake to write down what you are given:

V1=2.00 L

T1=298 K

P1=745.0 mm Hg

The unknown you are solving for is P2 = 760.0 mm Hg and V2 = x.

T2=273 K

The formula should be set up to account for the unknown:

P1V1/T1 =P2V2/T2

## Combined Gas Law Formula FAQs

### What is the formula for Combined Gas Law?

The combined Gas Law is formed by the combination of three gas laws, namely Boyle’s law, Charles Law, and Gay Lussac’s Law. The overall formula is given as PVT=K.

### Who founded the combined gas law?

The prehistoric gas laws were unified into a single law known as the combined gas law by French scientist Benoît Paul Émile Clapeyron in 1834.

### What does the combined gas law in cloud formation include?

The production of clouds is yet another instance of using combined gas laws. Water is heated to create water vapor, which rises into the atmosphere and is condensed and cooled, expanding the volume and forming a cloud.

### Is the combined gas law a constant?

Experimental research has shown that, while the temperature is held constant, the volume of a given amount of gas is inversely proportional to the pressure applied to it.

### What are the combined gas law's applications?

In real life, the coupled gas law has useful uses. This rule is in effect when pressure, volume, and temperature vary but the amount of gas is constant. For instance, the law predicts the behavior of air conditioners, refrigerators, and clouds.